I'm sorry but I can't "buy" this etymology at all. "Ta ta" also gets written off as baby talk. If you spend a few weeks in the north of England, you'd quickly realize that "ta" has nothing to do with babies.
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Ian AtkinDec 10 '12 at 6:59

My compact version of The Oxford English Dictionary lists it as "An infantile word expressing thanks," and dates its first reference from 1772, unless my eyes deceive me (I am momentarily unable to locate the magnifying glass that came with the tome).

Edit:

Thank god for Eric Partridge. He quotes the same OED reference, only in larger type. Here is the entry:

When a term originates in northern English dialects as "ta" appears to, I often begin by looking at nordic languages as much of northern England was conquered by the Vikings and the parts of the language endure both in words and in the overall sound - if you listen the geordie accent has a definite scandinavian cadence to it.

Looking at modern Danish and Norwegian we see that "Thanks" translates as "Tak" or "Takk" respectively, so it seems to me quite plausible that this provides an origin for "Ta".

The burden of proof is on the one claiming an explanation to be true. :-) The fact that etymological dictionaries don't list this Viking hypothesis is enough, for now.
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ShreevatsaRDec 8 '10 at 5:00

Right! I shall use my considerable knowledge of norse languages ( specifically none ) and the considerable libraries at my disposal ( specifically I think there is one somewhere in town, but it only has a few paperbacks ) to prove it directly!
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glenatronDec 9 '10 at 16:35

+1. Very probable explanation. For the words of the baby/kid talk dictionary are very old. The only older group of names are probably the names of the rivers
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GangnusOct 2 '13 at 16:34

As an Australian I can say 'ta' is used extensively in Australia. I can't comment on other explanatios as I am not a language expert. However I would like to suggest, as that many caucasian Australians are of Celtic ancestry, that the possible origin of this word is from the Irish galic word for 'yes' (tá). If you think of 'yes' in a broader context; and as and an affirmative response (i.e. Yes) to an action, it kinda makes sense. Just my thoughts, any comments on this welcome.

Tá does not mean yes. It means is. The Celtic languages do not have distinct words for yes and no. Instead, one replies with the verb; in that context (after a question beginning an bhfuil), tá can mean yes.
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TRiGDec 19 '11 at 21:56